A New Longwave Mode Propagator for the Earth–Ionosphere Waveguide

Very-low-frequency (VLF) radio waves propagate efficiently over long distances in the naturally occurring Earth–ionosphere waveguide. These radio waves are emitted by both natural and man-made sources and have been used for navigation and global communication systems and as a means to remotely sense the lower ionosphere. Propagation models are required to design and analyze longwave radio links and act as a forward model in the nonlinear inversion of receiver measurements to estimate the ionosphere. We have developed software that applies a mode theory to calculate the distant fields produced by a dipole emitter in the Earth–ionosphere waveguide. This model, released as the Julia package LongwaveModePropagator.jl, is similar to the Long-Wavelength Propagation Capability (LWPC) but replaces the mode solver with the global complex roots and poles finding (GRPF) algorithm. As a result, mode finding is more robust and the model is simplified by solving the physical mode equation. This article presents an overview of the model physics and validates the new longwave mode propagator by comparing results with different ionospheres to LWPC and a finite-difference time-domain (FDTD) propagation model. As an example of its use, we briefly explore the relationship between exponential and Faraday-International Reference Ionosphere (FIRI) electron density profiles.